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It’s the Friday Puzzle!

Our little experiment was fun and interesting. It was a kind of a wisdom of the crowds thing, and examined the accuracy of the mean of people’s guesses. The average of the group was 44.58%. At 10 p.m. last night 38.30% of people had chosen BLUE, so the group was reasonably accurate. Stephen Motson was closest with 38.34% (email me and I will get a book to you).

I hope that you enjoyed it and thanks for taking part. So, to the Friday puzzle….

You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, how can you determine which coin is counterfeit using the scale only twice?

As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

That’s not the one I meant. Several weeks ago, Richard gave a puzzle, but never gave the answer. Instead, he said the one who gave the best answer would get a prize (one of his books, IIRC), but I never saw it awarded

No it doesn’t. Use the scales in the conventional way with something on each side. (Put your chosen coins on in one go – not individually) And repeat once. It is not a trick question and doesn’t require any jiggery pokery.

Now for a bonus : you need to determine your uses of the scale beforehand. In other words, you don’t have the result of the first weighs when you decide which coins to put on the scale the second time.

Initially thought I was reading the more famous “three bags” problem, which any Columbo fan knows by heart! (And I can still recall, very fondly, his tortuously drawn-out demonstration of the answer to that one). Hadn’t come across this variant before, and was initially stumped, but a quick sketch on paper illuminated the very elegant answer. Yes, it also works with nine, but I would argue that eight is the better number to set the problem with.

There’s a more common version of this problem that states you have 12 coins and a simple balance and that the fake one is a different weight. What’s the minimum number of balance operations to find the fake coin and how do you do it?

I initially thought it would require three weighings (4/2/1), only after cheating and looking it up did I realise the ‘trick’ (which, incidentally, does involve using the scales in the conventional manner to compare the weights of the coins).

Wow! Because you told me it was slightly heavier, I got the answer in about 7 seconds (all conditions) but I have seen similar puzzles before. The harder question is where you don’t know if it is heavier or lighter…

With regard to the average guess being ‘reasonably accurate’ that’s incredibly generous. Over 6% different is way out, especially when you would expect that if someone had guessed a mean value higher than 0.33, they would then probably vote blue themselves to push the mean up and improve their chances of winning the prize. I’m surprised that the actual mean didn’t end up being a lot higher.

Out of interest would you say that practicing such puzzles has had a positive impact on your puzzle solving ability? By which I guess I mean, easier to think laterally, ability to see more variations, quicker to home in on the answer?

Who has hijacked this website, and where has he hidden Richard Wiseman? The last three weeks’ puzzles have all been very easy and straighforward, without any of the usual naughtinesses or ambiguities. Something must be wrong.